Swindling at Chess

The idea of "swindling" refers to trying to turn around a losing game, so that you either win or at least draw.
This isn't actually cheating, it's trying to win or draw within the rules by having your opponent make a mistake.
Some of the common swindles in beginner chess are:

Just Wait for the Next Mistake: It happens all the time. Just keep playing, don't give up, wait for your opponent's next mistake. Countless beginner games see-saw between wins and losses.

Attack the King: If you get their King, you win, regardless of how many extra pieces they have. So if you're down, just start bringing your pieces toward the enemy King.
Go for the checkmate. It has a very good success rate.

Play Complex Tactics: If you're losing, it's usually better to play complex, tactical, trappy chess.
Avoid piece swaps.
Play actively and aggressively.
Look for pins, forks, skewers, and other tactical tricks.
Don't just play quietly and let your opponent swap all the pieces until the game is down into an easily won endgame.

Unbalance the position: If you're down quite a bit of material, it can be worthwhile to create an unbalanced position. Make your pieces different from their pieces. Like swap a Rook for a Knight and Bishop, or vice versa. Or try to swap your Queen for a Rook and Knight/Bishop, or 2 Rooks, or whatever uneven swaps you can arrange. Having an unbalanced position creates unusual and complex situations, which can be trappy.

Swap pawns but not pieces (Keep your pieces): Generally it's better to keep more of your pieces. Avoid swaps of pieces. But swapping pawns often helps to draw later in the endgame. Having more pieces also means more possibilities for active play, attacks, traps, tactics, combinations, etc.

Play for Time: It often happens that the player who's winning is also the player who's short of time on the clock. You can win on time even if you're losing on the board.

Draw by Stalemate: No matter how many pieces you are down, if your opponent stalemates you, it's a draw.
To play for stalemate, you need to get rid of all your pieces, and block up all of your pawns.
Push your pawns until they get blocked or captured.
Then you try to get your King trapped in the corner or against the side of the board.

Offer a draw: Even if your opponent is winning clearly, they might decide to play it safe by accepting a draw.

Advanced Endgame Drawing Techniques

If you're down material, like a pawn or two down, there are some types of endgames that are more likely to draw.

Rook endings: Rook-and-pawn endings are often drawish (and also "trappy").

Pawnless draw: Get rid of all the pawns:
Pawnless endings are often drawn.
So if you can swap off all of the pawns, many endings without pawns are drawn (because your opponent can't make a new Queen).
The less pawns there are on the board, the more chances for a draw.
(Note: that means swap pawns, but don't just throw away your pawns!)

King-and-pawn versus King: The endings with just 3 pieces, where one player has a single pawn, and just the kings, are surprisingly often drawn.
Learn how to block the opponent's pawn and draw.

Queen versus Rook Endings: Really down like a whole piece? Three or four pawns down? The ending with the greatest drawing chances and a big material disparity is to have a Rook versus your opponent's Queen.
So if you're down a Knight, try to give up your Queen for a Rook-and-Knight, then you have a Rook versus the enemy Queen.
Won't work if you have weak pawns that the Queen will chomp, but if your Rook can protect your pawns, it's hard for the Queen to make progress.
Even without any pawns, Queen-versus-Rook endings are theoretically won but very hard to win in practice, just try it!
And if there's pawns, a Queen-versus-Rook-and-two-pawns often ends in a draw with a fortress set-up.
Very tricky endings to win, even with the powerful Queen!

Really Sneaky Swindles

You didn't hear about these from me...

Unexpectedly bad moves; Sneaky touch move tricks: If you intentionally play a silly move, sometimes people will just reflex touch a piece without thinking.
For example, if you check their King, they might immediately touch the King.
The nasty way to use this for a swindle is having the checking move also intentionally being an obviously silly attack on the opposing Queen or Rook or whatever.
It's like a fork, only a lot dumber.
Rarely works in practice!

Take their King: In lightning chess, it's legal to take the king.
If your opponent is preoccupied with Queening their extra five pawns on the Queenside, they might not notice if you check their King on the other side of the board. And then you simply take their King on the next move! (Hint: You don't have to say "check" when you check their king.)

King takes King: Only have a King left in a game of lightning? You can still swindle. Wait till they're busy elsewhere. Then just walk your King over to their King and take their King. Amazingly, this sometimes works!

Really, these tricks are awful; don't use these in tournaments.
Save them for your social games with friends!